Re: Existence, Self-identity and Uniqueness.

On Wed, 27 Dec 2006, Jan Burse wrote:

Owen wrote:
Within first order predicate logic with identity, we can show that
these terms (Existence, Self-identity and Uniqueness) are equivalent.
E!(the x:Fx) <-> (the x:Fx)=(the x:Fx) <-> U!(the x:Fx).

It looks you have fetched an old book with some iota
calculus in it. Iota calculus has the problem that
you cannot substitute equals for equals any more.

He's rehashing iota stuff onto ontological orneriness.

One can easily see that:

the x:Fx = y -> (A(the x:Fx) <-> A(y))

is only ok, when Fx has a unique x.

Ie, when E!x F(x)

But when Fx has not a unique x, then A(the x:Fx)
becomes false. Here is how this can happen, when
a unique x does not exists the precond becomes
false, hence:

The definition of G(ixF(x)) encompasses or implies E!x F(x).
For example it may be define, or defined equivalent to
ExG(x) & (Ax,y)(F(x) & F(y) -> x = y)
Thus
ixF(x) = y -> E!x F(x)

So I see not the objection.

.

Loading